A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. The 95% confidence interval for the population mean SAT score is
A) 1340.06 to 1459.94.
B) 1341.20 to 1458.80.
C) 1349.93 to 1450.07.
D) 1320.32 to 1479.68.

Question

Quizplus · Accepted Answer

The correct answer is A because the 95% confidence interval for the population mean SAT score is 1340.06 to 1459.94. This interval is calculated using the formula: sample mean +/- 1.96 * (standard deviation / square root of sample size). In this case, the sample mean is 1400, the standard deviation is 240, and the sample size is 64. Plugging these values into the formula, we get: 1400 +/- 1.96 * (240 / square root of 64) = 1400 +/- 1.96 * (240 / 8) = 1400 +/- 1.96 * 30 = 1400 +/- 59.94 = 1340.06 to 1459.94.

A Random Sample of 64 SAT Scores of Students Applying